What is String Theory Good For (Part I)?

This is, I guess, my foray into the bloggy string wars (or the stringy blog wars?). But not really. I just want to give you some of my brief perspectives on why string theory is kind of a big deal. This will possibly precipitate screaming and gnashing of teeth in the comments section, but whatever. It is not my intention to get into some sort of flamewar (or whatever the kids are calling it nowadays) so I probably won’t respond to any comments.

A short list of what you might think string theory is good for.

1. Nothing–unlike a lot of my colleagues, I think this is a perfectly reasonable perspective. In fact, if you had this perspective about all of particle physics, I think it also would be perfectly reasonable. In short, what we do benefits absolutely nobody. We should all probably be using our brains to search for a cancer cure.

However, I find to stomach arguments that other completely useless things–like calculating the QCD beta function to n loops, or calculating the homotopy groups of spheres is somehow more worthy. Usefulness is not why most people engage in many areas of math and physics.

2. Deriving the Standard Model From–String theory requires extra dimensions in order for it to make sense. This isn’t as absurd as it sounds, because we haven’t probed (with big particle colliders) distances anywhere near as small as those short distances where a string theory is naturally defined. Therefore, it wouldn’t be surprising that we hadn’t observed these other dimensions, as they would naturally be small, on the length scale where the string theory lived.

A long time ago in a galaxy far far away (the 70’s and 80’s) people thought that maybe we could write down a string theory that was defined at very high energies (short distances), figure out the form that these extra dimensions HAD to take, turn the string theory crank, and be able to write down the theory of particle physics at much lower energies, where our particle colliders can reach–namely the standard model of particle physics.

However, it turns out that figuring out the form that the extra dimensions HAVE to take is really, really hard. There seem to be many possible forms that they can take, and no promise of uniqueness. This has resorted to some people talking about a “landscape”. I definitely will not talk about that in this post.

So while in theory, it’d be completely amazing if we could turn the string theory crank and get out the standard model (plus whatever comes at higher energies so that we could predict what we’d see at, say, the LHC), this seems very unlikely. This has caused some people to call the whole endeavor of string theory “masturbatory”. I enjoy any blog post or powerpoint presentation where I can use that word (so far 1 blog post, 1 powerpoint presentation).

3. Math–string theory and supersymmetric gauge theory have actually somehow given us ridiculous insights into pure mathematics. It’s absurd how much this actually works.

Someone (I forgot who, witten maybe) said that string theory is a great machine for mathematics conjectures. The basic idea is that one uses physical arguments, which everyone believes to be true (but for which there are no “proofs,” just lots of indirect evidence–an example of such a thing would be “Yang-Mills theory is confining”) and uses this to infer something about math.

One example where physics has been the existence of “mirror pairs” of Calabi-Yau manifolds. Another, very recent example, has been the Geometric Langlands program, which Witten and others are working very fervently on. However, since I have next to absolutely no idea what this is, I will not comment on it further. But as far as I can tell, its kind of a big deal.

One example that I do understand, since I’ve read the paper many times, is Hori and Tong’s “proof” of Rodland’s Conjecture: that the Pfaffian in the Grassmannian G(2,7) lives on the same kahler moduli space as a hypersurface Calabi Yau in a Grassmannian. The proof uses beautiful physical intuition about the dynamics of non-abelian gauge theories in two dimensions.

However, you may think that the kahler moduli spaces of Calabi Yau’s are useless. Fair enough, I say. But they’re quite beautiful.

Hmm…this blog post is getting rather long. Perhaps I shall turn it into two! So far it’s a bit lame though, because #1 was “nothing,” and then #2 turned out to be actually not that useful. And then #3 is rather beautiful but could be easily dismissed as useless. Do not think I am self negating, readers! I shall return with a sequel, where I hope to offer some other, more compelling reasons of why string theory is a beautiful, wonderful thing.

“figuring out the form that the extra dimensions HAVE to take is really, really hard” because they did some wrong turn at some point. It is pretty clear that SU(3)xU(1) lives in dimension 9, and SU(3)xSU(2)xU(1) lives in dimension 11. The problem is where does chiral SU(3)xSU(2)xU(1) live. Stringers abandoned the Kaluza-Klein idea, going instead for the broad field of SO(32) and E8xE8 gauge groups. Which really are no more than a gauged version of flavour, as Marcus and Sagnotti cared to tell.